Problem: Divide. Write the quotient in lowest terms. $5 \div 3\dfrac13 = $
Explanation: First, let's rewrite $5$ and $3\dfrac13$ as fractions: $5 \div 3\dfrac13 =\dfrac{5}1 \div \dfrac{10}3$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{10}3$ is $\dfrac3{10}$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{5}1 \div \dfrac{10}3=\dfrac{5}1\times\dfrac3{10}$ $=\dfrac{5\times 3}{1 \times 10}$ $=\dfrac{ \stackrel{1}{\cancel{5}} \times~ 3 }{ 1\times\underset{2}{\cancel{10}}} $ $=\dfrac{1\times 3}{1 \times 2}$ $=\dfrac{3}{2}$ We can also write this as $1\dfrac1{2}$.